1. Field of the Invention
Embodiments of the present invention generally relate to coding/decoding systems and methods and, more particularly, to channel coding and the corresponding decoding of signals, related to one-dimensional signals (e.g., time signals) as well as to two-dimensional signals (e.g., pictures), corresponding coding and decoding means.
2. Description of Related Art
Very popular and common are Reed-Solomon (RS) codes. Decoding of RS codes is purely algebraic, very difficult for the user to understand and not vivid; there is no general formula for the integration of soft decision methods. If application-specific optimisations of a complete system (with coding, modulation, channel, demodulation and decoding) are to be realised, the known (algebraic) coding and decoding has to be inserted as finished black box into the complete system; a system optimisation is possible, however, only around the box; really interlaced modifications which are, e.g., in connection with the used modulation method, and the application-specific integration of soft decision methods are hardly possible in practice. (Regarding soft decision, e.g., the demodulator may communicate to the decoder with which certainty the decision has been taken; the decoder uses this information for decoding by optimisation of a numerical certainty measure extending over a plurality of such decisions).
Recently, so-called turbo codes have been introduced and successfully used. With turbo codes two interlinked convolutional codes, separated by interleaving, are iteratively decoded by means of soft-in/soft-out Viterbi decoding. In certain cases turbo codes can decode surprisingly heavily disturbed signals, however, disadvantages are also involved: the iterative operating method leads to non-predictable computing time; turbo codes require convolutional codes with infinite impulse response (IIR). Such codes involve the risk of catastrophic error propagation. Good convolutional codes can be designed only in a computer-aided manner; there are no systematic design methods for “good” convolutional codes (even defining a quality criterion is difficult). The function of turbo codes is very difficult to understand. Thus, design and optimisation are very difficult.
The prior art of error correcting coding is described in R. H. Morelos-Zaragoza: “The Art of Error Correcting Coding”; Wiley 2002, ISBN 0471 49581 6.